New Metamaterial Mathematical Modeling of Acoustic Topological Insulators via Tunable Underwater Local Resonance

This study presents a new type of active underwater local resonance metamaterial mathematical model for topologically protected acoustic wave propagation. The underwater acoustic metamaterial consists of arrays of core cylinders coated with soft shells periodically located in a water environment. An efficient but simple computational model is established to analytically predict the system band behavior. Compared to a system with only Bragg scatters, two double Dirac cones (DDCs) are observed in the dispersion curve due to the local resonance mechanism. The result obtained from numerical analysis shows great consistency with analytical prediction. By tuning structural parameters, the four-fold degeneracy is realized at the center of the irreducible Brillouin zone, i.e., the Γ point. It leads to the generation of two dipolar states and two quadrupolar states. Motivated by the theoretical prediction, locations of the cylinders are tuned and the closing-reopening phenomenon of bandgaps in both higher frequency region and lower region is observed with topologically protected phase transition. Besides, it is found that two frequency domains for topologically protected interface modes (TPIMs) occur. It provides potentials for two passive working frequency ranges without structural reconstruction or active tuning of the system. The effects of temperature on TPIM behavior are also demonstrated. Both working frequencies of TPIMs can be easily tuned to different ranges without influencing the quality of TPIMs. Besides, robustness and defect-immune properties of the topologically protected wave propagation are exhibited. With temperature control, this smart system can be performed as an acoustic metamaterial switch device.